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The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.
Given:
- Candy costing $1.25 a pound is to be mixed with candy costing $1.45 a pound
- The resulting mixture should be 50 pounds of candy
- The resulting mixture should cost $1.30 a pound
To find: The amount of candy costing $1.25 a pound that should be mixed
Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.
Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.
Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.
Accordingly, the total cost of the resulting mixture is [tex]1.25x+1.45(50-x)[/tex]
However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is [tex]1.30 \times 50[/tex]
Equating the total cost of the resulting mixture obtained in two ways, we get,
[tex]1.25x+1.45(50-x)=1.30 \times 50[/tex]
[tex]1.25x+72.5-1.45x=65[/tex]
[tex]0.2x=7.5[/tex]
[tex]x=\frac{7.5}{0.2}[/tex]
[tex]x=37.5[/tex]
This implies that the resulting mixture should be made by mixing 37.5 pounds of candy costing $1.25 a pound.
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- When the candy costs [tex]\bold{\$1.25}[/tex] a pound, the candy store owner must use [tex]\bold{37.5}[/tex]pounds. [tex]\bold{\$1.25}[/tex] per-pound candy is to be blended with [tex]\bold{\$1.45}[/tex] per-pound candy.
- There must be [tex]\bold{50\ pounds}[/tex] of candy in the mixture So, the [tex]\bold{\$1.30}[/tex] per-pound ought to be the cost of a final mixture.
- This is the amount of [tex]\bold{\$1.25}[/tex] candy per pound which should be blended when 'x' pounds of candy cost [tex]\bold{\$1.25}[/tex] a pound, therefore the resultant combination must be constructed by joining 'x' pounds of candy together.
- The x pounds of candy costing [tex]\bold{\$1.25}[/tex] per pound must be combined with "[tex]\bold{50-x}[/tex]" pounds of candy costing [tex]\bold{\$1.45}[/tex] per pound because the total weight of its final mixture must be [tex]\bold{50\ pounds}[/tex].
- Later, 'x' pounds of candy costing [tex]\bold{\$1.25}[/tex] per-pound is mixed with '[tex]\bold{50-x}[/tex]' pounds of candy costing [tex]\bold{\$1.45}[/tex] per pound to achieve the desired mixture. As a result, the overall total cost of the final mixture is:
- [tex]\to \bold{1.25x+1.45(50-x)}[/tex]
- A 50-pound batch of a mixture will cost [tex]\bold{\$1.30}[/tex] per pound, and As an outcome, your total cost of the resulting mixture is [tex]\bold{1.30 \times 50}[/tex].
- It might calculate the overall cost of the resulting mixture by multiplying it by two.
[tex]\to \bold{ 1.25x+1.45(50-x)= 1.30 \times 50}\\\\ \to \bold{ 1.25x+72.5-1.45x= 65}\\\\ \to \bold{ -0.2x= -7.5}\\\\ \to \bold{ x=\frac{7.5}{0.2}}\\\\ \to \bold{ x=37.5}\\\\[/tex]
- It implies that [tex]\bold{37.5\ pounds}[/tex] of candy at [tex]\bold{\$1.25}[/tex] a pound must be used to make the final concoction.
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